Joist selection

Well, if I did the integrations correctly, the moment of inertia I_x
of a 4x8 missing the upper right quadrant is 22/15 times that of a
2x8. I'm a little surprised that the ratio wasn't smaller. I'm still
not sure if it is worth the trouble, but it is an interesting
exercise.

Yeah, it's the glue part that gives me pause, the old 2x4s are quite
rough, so I'd need a special glue that can gap fill, which seems like
a lot of trouble.
Cheers, Wayne

Wayne-
I didn't understand your ratio thing....are you saying that the 2x8
with a 2x4 attached (nailed or glued) is ~1.4 times stiffer than a 2x8
alone? The 22/15 ratio was a little obscure

a heavy spread of wood glue should easily fill surface of the old
2x4's or use a construction adhesive....adhesives are much better for
shear transfer than mechanical fasteners
by sistering the 2x8 to the 2x4 you'll reduce the deflection to 68%
of the deflection of the 2x8 alone.....so it wll go from 1/2" to ~3/8"
cheers
Bob

Depends on what sort of wood glue you're talking about. If you're
talking about Elmer's PVA, no, but if you're talking about
construction adhesive marketed for specific applications, like Liquid
Nails, or the PL brand of adhesives, they will work fine for you
application.
It seems to me that you're overanalyzing this thing. Two pieces of
wood have been attached with nails in shear for centuries with no
adhesive at all. Balloon framed houses used a ribbon/ledger to
support the floor joists with both being attached to the full height
studs with nails in shear only. They're not falling down. Your house
is from 1908 - prime balloon framing period. Is that how your floor
joists are connected?
Your low height attic load is far less and you're analyzing it far
more. And you'd already determined that the 2x8 on it's own would
take care of the load - it doesn't need the sistered 2x4 to do the
work, so the nails in shear won't be doing a hell of a lot of work.
The glue question is like a guy wearing a belt and suspenders asking
if he needs overalls to keep his pants up.
The only small wrinkle was the 1x4 plate resting on top of the CJs
requiring the notch. You'd already established that shear and bearing
area weren't issues as a single 2x6 was adequate. Since you will have
double the sectional area there's really no question of the notch
being a problem. In balloon framed houses it's not uncommon to have a
flush beam or two supporting the inboard ends of the first floor
joists. The standard way of doing that, before the introduction of
joist hangers, was to nail a 2x3 ledger flat to the side, and flush
with the bottom of the flush beam. The FJs were notched to rest on
the ledger and toe-nailed to the beam. The notch on the bottom is a
_much_ bigger issue than a notch on the top, yet even though you'll
often see splits at the notch when you dissect the house, you rarely
see failures.
My concern with the deflection is due to the fact that I don't
consider 1/360 adequate for a floor. That's code - code is the
minimum acceptable - I don't build that way. People also don't _live_
that way - particularly not with attics. A live load of 30 PSF in a
bedroom is reasonable. People need to move around in a bedroom, and
they don't pile stuff on every square foot of available floor space.
That's not the case for an attic.
It wasn't clear from your earlier posts exactly how much room (height
and area) is in the attic, and it wasn't clear what would be stored
there. A single liquor bottle size box of books can weigh more than
20 PSF, and, if there's room, people stack stuff in an attic. If you
can guarantee that the attic will never see more than the 20 PSF, even
after you sell the house or kick the bucket, then fine - otherwise, go
with a more conservative load and a more stringent deflection
criteria.
As an aside, we could have gotten to the meat of the matter a lot more
quickly if you'd posted a picture of the situation and/or given more
complete information upfront.
Note to BobK: You said nails weren't good in shear. What does that
mean? I had a building inspector say the same thing to me - I didn't
want to argue with him just because he was wrong - he's the building
inspector and the nails in shear wasn't an issue. You I can argue
with! ;) What's your argument against nails in shear?
Okay, that's all for now. I'm hungry and I'm not going to proof read
- let me know if any inanity worked it's way in. ;)
R

Well, I think I narrowly framed my original question (double 2x6s or
notched 2x8s), and we pretty quickly got to the practical answer (use
tapered 2x8s). However, people were interested in the whole story, so
I've been happy to provide the extra details. That has led to some
interesting side questions, which are perhaps less practical.

No, it's platform framed. The only weird detail is the 1x4 plate
between the ceiling joists and the rafters.

Just to be clear, I won't have double the sectional area. I'll have
the sectional area of a 2x6 after I do the tapering. If I want to
sister the existing 2x4s and consider its sectional area, then I have
to be concerned with the sistering details. But since even the single
2x6 is deflection controlled, there is "reserve" sectional area there,
so I'm not concerned about the possiblity of stress concentration from
the tapering.

So what do you consider adequate? Will my skim coat plaster ceiling
crack under a live load deflection of L/360?

The roof is hipped at an 8:12 slope, so over the 8' region, the
clearance at center span varies from 0' to 5'4" or so. I'm not
actually storing anything up there, my real concern is about the
deflection from a person standing (squatting) on a single joist. As
for others storing stuff up there, I guess that's why the building
code requires a 20psf live load where the clearance exceeds 3'6". I
think that's adequate in this situation.

I don't know about that, the meat of the matter from my point of view
was in my original question, that's why I specifically made it as
short and constrained as possible.
Above all, I appreciate the time and attention shown in your
responses, they reflect the practical experience that I lack.
Thanks, Wayne

The 'extra' details are usually the things that determine the best
solution. There seems to be a bell curve to newsgroup questions.
Newbies leave out all the pertinent information, then have to fill it
in when people point the necessity of the omitted information.
Posters with a bit more posting experience, but maybe not more
technical information/experience, post more information up front.
Posters with more technical experience often try to simplify the
question to the one issue that concerns them. This leads back to the
'insufficient information for meaningful response' replies.

That was the low blood sugar talking. Sorry about that. Should have
said _almost_ double the cross section. I don't any practical
advantage to the tapering in your particular situation. This is what
BobK wrote in his first reply:
"You might consider a taper cut rather than a sharp cut out.
Timber is happier if you avoid abrupt section changes but in this
case the local stress state appears to "compress" :notch rather than
wanting to split it open."
I agree with the second part of the last sentence, and the
_generality_ of the first part. Your situation won't benefit from
tapering. It won't change any stress state. The same way doctors are
supposed to "first, do no harm", carpenters are supposed to "not
remove any wood without a reason." In your specific situation there
is not reason to do it, so why do you want to do it? You should
listen to BobK. ;)

Eventually. They all do. I don't think you're taking a big risk, and
frankly if you're not storing anything up there you're not taking any
risk at all. You could do me a favor though. After the supplemental
CJs are in place, take an elevation of the bottom of a central joist
at midspan. After you have rocked and plastered, do it again. I'm
curious to see what sort of deflection you get from just the dead
load.

For you, yes, I agree. Do not doubt that someone will do something
stupid in that attic in years to come.

And therein lies the rub. You were able to inspect the situation
firsthand and have way more information to help make a decision.
Playing detective requires me to ask questions - some of which will be
dead ends. I still have to ask them. The more experience I get the
more finely tuned my analytical skills become. These newsgroups help
me develop those skills and hopefully save somebody a 'learning'
experience.

OK, that is what I was trying to do, sorry if I wasn't successful in
simplifying away the extraneous details while still providing the
necessary details.

After thinking about it, I believe there will be a benefit as far as
installing the new joists. Since they will have to fit between the
wall top plate and the rafter 1x4 plate on both ends, I believe I'll
have to put them in place flat, one end at a time, and then turn them
upright. That would be hard to do if they are notched to fit tightly
between the two plates. With a taper, the interference will be
confined to a fraction of the thickness of the wall. Of course, that
still may make it difficult. :-)

The weight of the 1/2" gypsum board is 2 psf, and I believe 1 psf
would be generous for the skim coat plaster. So at 3 psf, the
calculated deflection is 3/20 * 0.5" = 0.075", or 0.05" if I
succesfully sister the existing joists. As to measuring it, that
might take me six months, so we'll both have probably forgotten by
then. :-)

Well, there's a limit to what I can do. It seems like it would be
fair to match the stiffness of the ceiling joists before I removed the
wall, and the stiffness of the ceiling joists in the rest of the
attic. A quick check shows that both of these are/were at about L/360
deflection for 20psf live load, which is what I'll be providing.
Cheers, Wayne

I'm not BobK, but I took this comment to mean that nails are not as
good as adhesive when you want continuous shear transfer. And that
you need continuous shear transfer to make the pieces of a built up
beam act as a composite section. That's a different story than
nailing a ledger to a stud wall, where the members are only
overlapping in a small area.
Cheers, Wayne

Wayne-
You're not me, you should thank goodness for that :)
but your answer

good as adhesive when you want continuous shear transfer. And that
you need continuous shear transfer to make the pieces of a built up
beam act as a composite section. That's a different story than
nailing a ledger to a stud wall, where the members are only
overlapping in a small area. <
was spot on to what I would have written
R-
I checked my posts & didn't find a direct reference to nails in shear
being "not good"
but if I did, I was / am wrong.
Nails are fine in shear, I have no argument with nails in shear,
that's what they're meant for (just not for withdrawal)
I have no idea what that building inspector was thinking... ?????
but where one needs continuous shear transfer to develop composite
action (built up box beam, I beam, etc) adhesives are much better
than discrete mechanical fasteners because the stress is well
distributed and the shear connection is stiffer than nails.........but
since I often do "belt, suspenders, staples & duct tape"....... I
prefer adhesive AND fasteners. :)
Also.guilty........Wayne & I tend to over analyze things
(him more than me, because he has less experience but he CAN do
thecalcs & ask lots of questions...me, because I'm always looking for
"better / optimum".
cheers
Bob

And why exactly do you need the shear transfer in your situation? You
don't. You've already established that the new framing members can
take the load on their own. There's little reason to tie the new CJs
to the old so you don't really need adhesive, or nails for that
matter.

But you don't need the existing 2x4s, so there is no reason to be
concerned about shear transfer, right? Stiffness attracts load, and
the 2x6s or 2x8 will be far stiffer than the existing 2x4. The 2x4,
if sistered, won't be called on to do any work until the 2x8 has
deflected enough that the 2x4 becomes involved, and that won't happen
with a 1/2" deflection over a 17' span.

This is where theory and reality vary. I have no argument that two
structural members that are attached continuously and not at isolated
points, will do a better job in shear transfer. But there have been
bolted and nailed composite beams in use for a long time - they're not
failing.
So what does the adhesive add in this situation? Expense and time
wasted. If the beam was in a more critical location, I'd agree with
the belt and suspenders approach. In this specific situation there is
absolutely nothing gained.

Me neither! He's a nice guy, though, so I let him slide. Interesting
thing about his building department though - they had a big scandal a
little while back. Four separate guys got busted for shady dealings -
one of them was the commissioner. None of the guys knew what the
other ones were doing. One guy, and you'll love this, refused to
inspect/approve a homeowner's drywell installation until the homeowner
bought four tickets to some firemen's benefit dinner! WTF?! So, for
$900 or whatever it was - money he never saw, this guy threw away his
career and is facing potential jail time.

Better/optimum also takes into account expense, effort and added
benefit. I fail to see how construction adhesive affects any of those
criteria in a positive way in Wayne's situation. If you just want to
say, 'But it makes me _feel_ better!', then I wouldn't argue.
R

OK, we have that the new 2x8 joist alone is deflection critical but
adequate for the 16'5" span. Some have suggested that the 1/2"
deflection this gives under live load is too much for that span. :-)
So the question was raised of how to use the existing 2x4 joist to
stiffen the new 2x8 joist. A few comments:
First, you statement "stiffness attracts load" is true when members
are acting compatibly (same deflection) but separately. This would
apply if the 2x4s are left in place, unattached to the 2x8s, and we
considered that the gypsum board was sufficient to give equal
deflections.
In this case, the moment of inertia (b*h^3/12) of the 2x8 (at 1.5" by
7.25") is six times that of the 2x4 (at 2" by 3.625"). So the overall
system stiffness is 1 + 1/6 = 7/6 = 1.16 times as much as the 2x8
alone.
However, if we adequately tie the 2x4 to the side of the 2x8 (bottoms
flush), such as by using frequent smaller nails, or a good adhesive,
then the two members will act together as a composite section. This
composite section, from the previous discussion, will be 22/15 = 1.47
times as stiff as the 2x8 alone.
This difference arises because the two members are different heights,
and we are attaching them off center. In the more typical situation
of both members being the same height, (a 2x8 sistered to a 2x8), the
two calculations would give the same answer (twice as stiff). This is
behind your experience that sistering without adhesive works fine.
Similarly, if the 2x4 were attached to the 2x8 so their centerlines
were at the same height, then again both calculations would give the
same answer (1.16 times as stiff).
Lastly, as to the question of adhesive versus many small nails, I have
the recollection that under load the nails will have an initial nail
slip before being full engaged, while the adhesive won't have this
initial slip. So in a deflection critical situation, the adhesive
will work better. If the sistering is to increase strength, and the
fastening is just to share the load, the difference is not important.
I'm not 100% sure my recollection here is correct, perhaps BobK can
confirm this.
Cheers, Wayne

Wayne-
Thanks for posting this...my PC is acting up & I've lost a couple post
before I sent them.
I hope you're not making Rico's head hurt with those numbers, mine is
hurting :)
Be careful your post are starting to look a little like Nick's from
Villanova. :)
You're spot on about sistering vs composite beam construction....we're
talking about making an asymmetric T - beam.
In a true sistering situation a handful of nails & you're good to
go.
In your situation we really want the 2x8 & the 2x4 to act as if
they're the same piece of timber. If my memory serves me you need
something like 100 psi or more in wood to get that behavior...pretty
hard to do with nails.
btw when I retrofitted my attic joists (2x4's) I glued (epoxy) & osb
cleated members onto the top edges of the existing 2x4's to create
~2x8's
I did this crazy thing because I had used redwood 2x6's leftover from
a job from 10 years ago. The glued "top sistered" joists were stiffer
than the 2x6's & I saved 2" of attic headroom that was critical.
I glued (brushed clean, no clamping, no cleats) test members together
& tested them to failure. Glue stress at failure 173 psi shear.
Based on my calcs & testing the attic joists are ~6x stiffer now &
can easily handle an attic storage load. :)
cheers
Bob

You might want to think about your plasterboard layout and where you
will have seems it'd be a good idea to glue and nail the sisters just to
make sure there is no movement.
The rest I would just nail in place. Glue is a waste of time, IMO.

Creating a composite beam out of the 2x8 & 2x4 combo (with glue &
nails) increases his joist stiffness by 50% which goes in the
direction that you suggested....L/360 may not be stiff enough, L/520
is better.
Since his ceiling is unloaded....if he creates this composite
asymmetric T beam he will get the added stiffness benefit. ....and
his plaster may have a better chance of survival.
IMO a 50% increase in stiffness is worth the extra work (if you really
think that L/360 is too limp then you should also agree that a 50%
stiffness boost is worth it)
BTW tapers are elegant,
notches, esp when the kerfs intersect or they're made with saw &
rigging axe
are ugly...... :)
cheers
Bob

Wayne-
Your 22/15 ratio is making this old engineer crazier than I normally
am.
A simple "factor of 1.5x stiffer" would be be easier for us practical
types to parse.
That said, yeah, the sistering is a little more work
but with caulk tube dispensed adhesive, some set up clamps, shoot a
bunch of staples or brads, remove the clamps & move to the next
joist. You've only got five joists to do.....
"cost of quality vs cost of non-conformance"
how upset will you be when the ceiling finish cracks?
your 2x8 is deflection controlled, you've got lots of strength but the
plaster finish wants stiffness........ you'll get L/520 instead of L/
360
If you really want to "geek out" ....check the joist slope as a
function of span for your assumed loading condition & compare to
suggested limits for brittle finishes.
it's not really deflection that matters but changes in deflections
cheers
Bob

OK, I'm a mathematician, but when I'm doing engineering, you are
right, I should say 1.5 because that easier to understand and 1.5 22/15 within the accuracy of our modeling of reality. :-)

I feel like I'll have to shoot at least 0.131" nails. I mean, I don't
think the prescriptive building code recognizes construction adhesive
as a substitute for nails?
BTW, is it fair to say that the adhesive connection is stiffer than
the nail connection because the nail connection has an initial
slip/crushing before it gets fully engaged?
Cheers, Wayne

Wayne-
I was just kidding you....I know your the mathematician. :)
Those ratios make my head hurt...I think in factors & %'s.
Rico's hammering us (& rightfully so) ..........are we really adding
any real performance benefit if you sister the old 2x4's to the new
2x8's? Yeah, the composite will be 50% stiffer, but do you need it?
In another post you state that the new 2x8's are stiffer than the old
in place unmodified 2x6's. If that's so then you really don't need to
add the extra stiffness beyond the new 2x8's
But
if the old 2x6's are stiffer than L/360 & the new 2x8's are stiffer
than L/360
BUT if the new 2x8's are less stiff than the old 2x6's ........you'd
be reducing the framing stiffness & the plaster MIGHT be unhappy.
In another post you state....

deflection for 20psf live load, which is what I'll be providing. <<<
you'll be fine as long as your new installation in reality is at least
as stiff as the old one.
Another thing to consider, old growth DF has a higher elastic modulus
than currently available new timbers. I sat on a committee with a
REALLY old engineer (old enough to be my dad) & he'd sometimes spec
the number of growth rings per inch on bending members!
Your comment about nail size.....I like smaller nails, they damage
the wood less than larger nails. In fact .148 is about the largest
nail I use unless I'm using VERY large timbers. Based on my research .
148 is about the largest nail that 2x's & 4's will accept without
damaging trauma to the wood. I've tested lots of timber connections &
large nails too close together (code allowed spacing is often too
close) will create a connection that is weaker than smaller nails.
Additionally since this composite joist exercise is really above &
beyond the code (you've already exceeded code min with the 2x8,
right?) you can do whatever you want. Yeah, .113's are a good
choice for "stitching" but I prefer a LOT of smaller
fasteners.......an infinite number of infinitesimally small fasteners
would approach the behavior of adhesive :)
My fastener of choice is a 16ga staple or 16ga brad but the .113 is ok
too.

connection because the nail connection has an initial slip/crushing before it
gets fully engaged? <<
Yup, that's why I prefer smaller fasteners & more of them. Smaller
fasteners have smaller localized loads on the timber. 16 gage staples
are good for ~250 lbs (per staple, ultimate shear failure load...lots
of slip. They have effectively zero slip at 50 lbs per staple)
Nails have slip, glue doesn't; glue can be brittle & can fail, nailed
connections are ductile & typically do not fail....that's why I
combine them.
cheers
Bob

Rico needs it, as he says L/360 isn't stiff enough. :-) Based on the
discussion I see it as a small definite improvement, when the time
comes next week I'll figure out if it is worth the small definite
extra work.

Yes, that's a good thing, as the old growth DF is #2 or #3, while the
new members will be SS, so we can call it a wash. :-) Actually it's
not really a wash, as a few of the old joists have large knots on the
bottom half near midspan, that's really bad.

Assuming the old and new have the same E = 1.9 Mpsi and a 20psf live
load and 10psf dead load, the old 2x6s spanned 13'9" (good for 14'4"
at L/360 deflection) and the old 2x4s spanned 9' (good for 9'1" at
L/360). The new 2x8s will span 16'5" (good for 17'2" at L/360).
Everything is deflection controlled. So the new 2x8s will be just
about as stiff as the old construction.

Wayne-
Is the E for new growth DF really 1.9 Mpsi?
btw correct me if the NDS says (or you if know) but SS is about flaws
not a high E.
Old growth DF has very closely spaced growth rings & I was told that
wood density drives E not knots / flaws.
I'd bet on the E of the old timber being higher but the new SS having
few / no flaws.
Have you considered engineered timber? It can have some pretty high
E's.
cheers
Bob

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